L_q规则化趋势滤波

Regularized Trend Filtering With L_q Penalty

含有L_q罚函数的线性回归可以进行变量选择或者系数缩减,利用Lq罚函数的这种性质,可将H-P滤波和L_1趋势滤波推广为L_q规则化趋势滤波。在内在趋势是分段线性趋势(0<q≤1)和无折点趋势(q>1)两种假设下,使用LLA方法和凸优化技术进行估计,提出修正的GCV准则进行调整参数选择。数值分析显示,在不同的假设下,本文提出的方法优于H-P滤波和L_1趋势滤波。该方法可以有效地提取时间序列的内在趋势,也可以扩展得到其他形式的解,在时间序列分析中有重要的意义。

Penalized linear regression with Lq penalty can select variables or constraint coefficients. This paper makes use of the propertie of Lq penalty to extend H-P trend filtering and L1 trend filtering to Lq trend filtering. We research on two different assumption for underlying trend, which are piecewise linear trend when 0〈q≤1 and trend without knots when q〉1. We estimate them through LLA meth- od and convex optimization and also propose a modified GCV criterion for choosing the tuning parameter. The numerical analysis shows that, under different assump- tion, our method performs better than H-P trend filtering and 1.1 trend filte- ring. This method can extract the underlying trend efficiently and can be easily modified to adapt to other assumptions, thus it is of great significance in the time series analysis.